Rory,,,sorry,,but there is no way to bring in modern/contemporary without taking out the entire kitchen (cabs/flooring,stone). what you have and what you want are at two opposite ends. You have thick traditional crown molding, traditional hutch, French style cabinets, plantation type shutters, and a rounded granite island,,,all of which scream, 'traditional/french country". I just don't see how doing a modern backsplash, or painting the cabinets is going to update it to more modern. quite frankly, doing any type of modern style w/those floors and those cabs will look silly. Even if you painted your cabinets (and getting a pro to do those will be well over 6K) replacing the granite and backsplash (another 10K) you'd still have the shape and style,,,, The flooring will still be there. to tear up that and replace, add another 6-10K.
Embrace the french country look until you can save up enough to bring in what you want.
you may be able to do something w/the living room, but can't tell until you take a decent pic without the previous owners kids things in the room.
Q
Metal/wood. Earthy
Q